I left my answer on the reCAPTCHA for the past 15 hours, just realized now. I agree that opaqueness is an awkward looking, sounding usage. As @SingerOfTheFall said, opacity as a noun just seems better. I would prefer structuring a sentence to use opaque instead of opaqueness if at all possible.
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Ellie KesselmanOct 18 '12 at 5:03

Whereas opaqueness was formed simply by adding the normal English derivational suffix -ness to the existing word opaque. Opacity has several senses and subsenses listed in the OED, while opaqueness has only the one I have provided above.

But as I said, the real difference is how often each is used relative to the other. This Google N-Gram shows that in actual printed use, opacity is favored over opaqueness by a favor of around 15 to 1:

Although these words aren’t normally made into plurals, they can be, and sometimes must be. Here the comparative euphony of opacities over the Gollum-like opaquenesses wins hands down in this other Google N-Gram:

In actual examples, here are the first three recent usage citations obtained by those N-Grams, first for opaquenesses:

It involves the acceptance of others by means of an indifference to, or neglect of, their differences, of all the opaquenesses and knobby protrusions that make it diflicult to swallow their souls into one's own. [citation]

He and Kistin had visited the hospitals once and seen briefly the doctorless, nurse- less place where those returning from enclayment were given a chance to cure themselves of the dreadful opaquenesses caused by lying, stealing, false pride, and the like. [citation]

Blackmur acquired great influence as a critic because he tackled the difficulties and opaquenesses of such modern poets as Yeats, Eliot, Stevens and Hart Crane head-on in a commentary that was subtle, discriminating, illuminating and ... [citation]

And then for opacities:

The opacities are classified according to the diameter of the predominant opacities: [citation]

In this system, the size, shape, and profusion of opacities on the radiographs of patients with penumoconiosis are classified in a detailed fashion by trained observers, using a set of standard radiographs. [citation]

Large capacities (greater than 1 cm in diameter) correspond to lesions of complicated pneumoconiosis (progressive massive fibrosis) and are classified into categories—A, B, and C—depending on their size. [citation]

"Opacity" is usually used in technical contexts, and invokes a nuance of it being a measurable quantity. "Opaqueness" is normally used when speaking colloquially, and can also be used metaphorically to mean "incomprehensibility resulting from obscurity of meaning" (Mirriam-Webster). To that end, it would sound strange to give an actual measurement of "opaqueness". For example:

I use opacity as a parameter between 0 and 100%, when describing the degree of transparency of something, most often web markup. For example, opacity = 0.2 would be very close to transparent, or "see through". A more typical value for my purposes is opacity = 0.8 which is only slightly transparent. Of course, a value of 1.0 or 100% means totally opaque, solid, not gauzy or translucent at all.

Opaqueness is more familiar to me as word used for prose communication, rather than webpage design. Although the word is legitimate, I don't find it easy to use in context. It seems more idiomatic to describe something as "more opaque" or "less opaque", although an example of usage of would be to say something had "an aspect of opaqueness to it".

not able to be seen through; not transparent:
bottles filled with a pale opaque liquid

(especially of language) hard or impossible to understand:
technical jargon that was opaque to her

Used figuratively, in an understanding = seeing the light sort of way, the two words can become very similar, as shown particularly by the Oxford Dictionaries entries.

Opacity also has several technical uses. As pointed out by several posters, it is used in programming. It is wrong to imagine that language exists only for programmers though - opacity also has a technical use in physics, and in linguistics, and in photography, and in the paint industry, and probably others that I am unaware of. For these localised uses it is probably better to ask in the appropriate forums.

-1: I think this is a spurious distinction.
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FumbleFingersOct 17 '12 at 13:31

This answer is confused and wrong. If, as you actually now illustrate, the adjective can apply to both understanding and optics then opaqueness can too (you offer no evidence to the contrary). This allows it the same range of meaning as Opacity, so then it just comes down to relative frequency of usage.
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itsbruceOct 18 '12 at 6:40

1

Usage is exactly whatvthe OP asked about - scroll up and look. OED lists obscurity as the main meaning for opacity and transmission of light for opaqueness. I understand that you consider yourself a higher authority than OED, but in reality the petty pedantry displayed by amateurs such as yourself is ruining this site. It should be a fun place to be, but it isn't.
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Roaring FishOct 18 '12 at 7:23